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LIBRARY OF CONGRESS 



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THE -. \l f/Af^^^ 

INTERNAtlOraL 

'I 

CORRESPONDENCE 

SCHOOLS. 

SCRANXON, PKNNA. 
o 

Instruction Paper. 

THIRD EDITION. 



^'^X<^'^^ SUBJECT: 

Mechanical Drawing. 



NOTICE.— The Student must, in accordance with his 
agreennent, treat this Paper as confidential. 



Entered according to the Act of Congress, in the year 1898, by The Colliery 

Engineer Company, in the office of the Librarian of Congress, 

at Washington. 



TMP96-024426 



Mechanical Drawing. 



DRAWIJSTG PLATE, TITLE : DETAILS. 

46. The first eight figures of this plate show the conven- 
tional methods of representing screws. The actual projection 
of a screw thread will be similar to the projection of the helix 
shown in Plate V; but, in order to save the time required to 
locate the pomts and trace in the curves, the following method^ 
are universally used, except, perhaps, in the case of screws of 
very large diameter and pitch, drawn full size. 

Fig. 1 represents a single square-threacled screw H 
inches m diameter, and f inch pitch. To draw the screw, first 
draw the center line m n, and a line A B at right angles to it 
Make the distance A B equal to the diameter of the screw or 
U inches, and through the points A and B draw lines A D Ind 
BE parallel to the center line ran. Also lav off on the line 
AB distances A F and B G equal to one-half of the pitch, and 
through the points F and G draw lines FH^nd GI parallel to 
the center Ime m n. These lines show the depth of the thread 
On the line AD, lay off the width of the thread and of the 
groove, AC, CJ, JK, etc., each equal to one-half of the pitch, 
or f X i = 3^ of an inch. Draw the line B C, and through 
the points ,/, K, L, M, etc. draw hues parallel to B C. Draw 
faint pencil lines through the points (7 and P, /and Q, K and B 
etc., to represent the back edges of the threads, and make the 
parts which are seen full lines ; then draw the lines TV,UW, 
etc. The method of drawing the remainder of the screw, and 



MECHANICAL DRAWING. 



the reason for using"tl^ri^ shade lines, as shown, should l,e 
apparent without further explanation. , , , f tl>P 

■I will be noticed that the width of the thread and o th 
Jore nieasnred parallel to the eenter line mn, a..d the dep 
: the thread are all exaetly the same; that is, they are each 
t'aUo oL-half of the pitch. If a section -e Jakeii ^^^^ 
the center line m«, the thread and groove -on d look 
Fig. 71, a series of squares ; hence the term .nuare *'»«" • 

lig 2 shows a doxxble square-threaded sci-ew 1^ inches 
in dLieter and with f of an inch pitch. The reason foi 
usinH double thread is' that if the single square thread were 
u ed the depth would be so great as to weaken the bolt or rod 
on which it was cut, and render it unsafe for the 
purpose for which it was intended. To prevent 
this, either the diameter of the rod must be 
increased or the thread must be cut of Uie s^ 
depth and thickness as a thread of half the pitch 
or in this case, as if the pitch were f of an inch 
X i = I of an inch, as in the preceding problem ; 
another thread of the same size and Pi** ■(* o 
an inch) must be cut half-way between these fi.^t 
threads thus giving a double thread. The pitch, 
or distance that the screw would advance ni one 
turn, would be f of an inch, the same as if it were 
a single-threaded screw of f of an inch pitch 
while the depth of the thread is only half as great. 
To draw it, proceed exactly as in the last figure. To 
get the direction of the hne B C, which in this f g;- .^Pj;;*^^ 
L projection of the bottom edge of the top of the ti n e d 1^ 
off A C equal to one-half of the pitch, or f X 4 = ^ oi an men, 
aL draw the hne B C. The width of the threa s and ^ove 
and also the depth of the threads, is one-fourth of the pitch, 

' ihlTgrtlfe'^inJir, L, M, etc. draw faint pencil liiies^^ 
etc to rrpresent the back edges of the threads, and -^|^«^ « -^ 

.t; which are seen full lines. Through the point K diaw a 
paitswnicnaie ^^^^^^^. j^^^^, ,„ „^ 

faint pencil line K R, at iignt angie. 

intersecting the line FH in a. and draw the hne Ta, 




Fig. 71. 






MECHANICAL DRAWING. 5 



represents the bottom of the thread. The remainder of the 
screw should now be drawn without any trouble. 

Fig. 3 is a single Y-tlireaclea screw IJ inches in diam- 
eter and having 7 threads to the inch ; that is, the pitch is I 
of an inch. Draw a cylinder IJ inches in diameter, having 
m n for the center hue. Lay off ^ ^, B C, CD, etc., each equal 
to the i^itch, or i inch. Do the same on the left-hand side. 
By the aid of the T square and 60° triangle make the angles 
A OB, FO'G, etc. The rest of the thread can be drawn by 
referring to the figure. 

Fig. 4 represents a screw exactly like the preceding one, 
except that the thread is left-handed, instead of right-handed as 
in the previous case. 

To ascertain whether a thread is left- or right-handed, hold 
the screw in such a position that its axis is horizontal. If the 
thread is right-handed, as it usually is, the angle which the 
edge of the thread makes with the horizontal on the right-hand 
side is obtuse ; if left-handed, it makes an acute angle with the 
right-hand side of the horizontal. No further instruction 
should be necessary for drawing the thread. 

Fig. 5 represents a double Y-tlireacled screw IJ inches in 
diameter. It has 3^ threads per inch ; that is, the pitch is 
1 mch ^ 3^ = f inch. The same remarks regarding the draw- 
ing of it apply here that were used in describing Figs. 2 and 3. 

^ Fig. 6 represents a section of a brass nipple. When the 
diameter of a nipple is given, the inside diameter is always 
meant, unless otherwise specially stated. The actual diameter 
of a nipple or pipe is very rarely given, but must be taken from 
printed tables. The nominal diameter of the nipple shown in 
the figure is 1 inch, but the actual inside diameter is 1.05 
inches ; from the table, the outside diameter is found to be 1.32 
inches, making the thickness .135 of an inch. Owing to the 
thinness of the shell, pipe threads are finer than the threads on 
the same-sized rods. The coarsest pipe thread is 8 threads per 
inch. The number of threads per inch on the nipple shown is 
Hi-. The thread is tapered to make a tight fit, and the length 
of the threaded part on each end is 0.52 -j- 0.53 = 1.05 inches, 
of which length the distance between a and h represents the 



() MECHANICAL DRAWING. 

perfect thread, while from 6 to c the thread is chamfered ; that 
is, it dies out gradually. To draw the nipple, make a sectional 
view as shown. DraAV a cylinder, having mn as a center line 
1.32 inches in diameter; lay off the inside diameter equal to 
1.05 inches, and draw A B and CD. Now lay off the diameter 
ifir equal to 1.26 inches. Then lay off the distances iZ'Jand 
KL, equal to 0.52 -f- 0.53 =-- 1.05 inches; join the points H 
and J, and K and L, by straight lines representing the top of 
the threads. Now^ on the center line m yi, or on any line 
parallel to it, lay off a distance of 1 inch from the line A C 
downwards. Divide this distance into 11 J parts by means of 
the method given in problem 6, Art. 31. Project the points 
just found upon HJ, and, by means of the T square and 60° 
triangle, draw the threads from H to J as though all the threads 
were perfect. Draw^ the threads on K L in the same manner, 
remembering that the divisions on HJ are to be advanced half 
a thread, as shown ; that is, the top of one thread and the bot- 
tom of the preceding thread on the other side Avill be on a 
horizontal line. Now lay off the distance ah equal to 0.52 
inch, and project it on lines drawn parallel to KL and HJ, 
and touching the bottom of the threads. From the points of 
intersection draAV straight lines to J and Z, in order to obtain 
the bottoms of the imperfect threads extending from b to c. 
Complete the rest of the drawing in the same manner. 

Fig. 7 shows another method of representing a Y-threaded 
screw. This method has the advantage of making a neat-look- 
ing drawing, and of being very rapid in delineation. The pitch 
is laid off as in the three preceding figures. The heavily shaded 
lines represent the bottom of the thread, and their lengths are 
determined by constructing an equilateral triangle on the pitch 
distance as shown, and limiting the line to distances between 
two corresponding vertexes of the triangle. The diameter of 
the screw is 1 inch, and the number of threads per inch is 8. 

Fig. 8 represents the same screw shown in Fig. 7, but the lines 
indicating the bottom of the thread are left out altogether. 
This method is used on drawings where haste is necessary. 
Unless in very much of a hurry, the method shown in Fig. 7 is to 
be preferred. Ordinarily, when drawing screws as represented 



MECHANICAL DRAWING. 



by Figs. 7 and 8, it is not customary to lay off the pitch and 
the depth of the thread as above mentioned — the distances 
between the hnes representing the threads are simply gauged 
by the eye ; practice will enable this to be done very quickly 
and accurately. 

Fig. 9 shows two views of a small hand-wlieel. To draw 
it, locate the center (9, and through draw the center lines t r 
and 771 n at right angles to each other. From as a center, 
with the compasses set to the radius of the wheel, or 3J inches, 
draw the outer circle of the rim ; then, la}^ off the thickness of 
the rim, which is f of an inch, and draw the inner circle. 
Through 0, with the T square and 60° triangle, draw the center 
lines .4 B and CD. With as a center, draw two circles, one 
having a diameter of f of an inch, to represent the hole, and the 
other a diameter of IJ inches, to represent the outside of the 
hub. To draw the arms, make the chords of the arcs a b, c d, 
etc. each ^ inch long. Make the chords h I, i k, etc. each f inch 
long, and draw I b, h a, k d, etc. With a radius equal to J of an 
inch, describe the fillets, or arcs. A' B', CD', etc. tangent to the 
arms at A', B', C, etc. With a radius equal to ^ of an inch, 
.describe the fillets or arcs tangent to the inside of the rim and 
to the arms. All of these arcs terminate at the point of 
tangency. The cross-sectioned part on the arm indicates that a 
cross-section taken oi E F would look as shown, that is, that the 
arm is elliptical. 

The other view shows a conventional method, largely used in 
drawing rooms, of indicating a section of the wheel. It is 
termed a conventional method because it would really be 
impossible to obtain a section like the one shown. Theoret- 
ically, the arm in this view should be sectioned, but, for con- 
venience, a section is imagined to be taken through the rim and 
hub on the line tv^ and the two arms are shown in projection 
as they appear on the line m n. Draw the center line p q and 
the sections of the rim, as shown. Draw the arms from the 
dimensions given. DraAv the hub as shown, using a radius of 
-^ of an inch to draw the fillets or arcs tangent to A B and to 
the arm ; make 0' H' equal to H in the other view,- and 
describe an arc through H' tangent to tlte two arcs just drawn, 



MECHANICAL DRAWING. 



which are tangent to AB and the arm. The rest of the draw- 
ing can be completed without further explanation. 

Fig. 10 shows a crank, which should be drawn without 
difficulty from the dimensions given. The pin is forced in, 
and the end riveted over at A B, to prevent it from being 
pulled out. 

SECTION lillS^ES. 

47. The method ordinarily nsed for indicating the different 
materials by means of section lines is shown in Fig. 72, in a 
series of small squares drawn according to the usual method of 
sectioning the material named at each square. 




Cast iron, as mentioned before, is indi- 
cated by a series of parallel lines equally 
distant apart. 




Wrought iron is sectioned in the same' 
manner, except that every alternate line is 
shaded. 




Steel is sectioned by drawing two lines 
close together, and the third line about 1^ 
times as far from the second as the second 
is from the first, and repeating. 




Brass is sectioned like cast iron, except 
that every other line is broken. 



Fig. 72. 



MECHANICAL DRAWING. 




Babbitt metal is sectioned like cast iron 



—but : 
qiiares. 



both directions, formino- little 




\\'ood is sectioned by a series of rings 
and radiating lines like the cross-section of 
an oak tree. 



Fig. 72. 



scai.es. 

48. When it is desired to make a draAving other than full 
size, special scales are used. Thus, suppose it is required to 
make the drawing J size ; then, 3 inches on the drawing would 
represent 1 foot on the object. Hence, if 3 inches are laid off 
and divided into 12 equal parts, each of these parts will repre- 
sent 1 inch on the object. If these parts be subdivided into 
2, 4, 8, etc. parts, each will represent J, J, i, etc. of 1 inch 
on the object. A scale of this kind is called a quarter scale, 
or a scale of 3 Indies to tlie foot. An eiglitli scale, or a 
scale of 1^ Indies to tlie foot, would be constructed in the 
same way, except that IJ inches would be laid off instead of 
3 inches. These scales are written 3" = 1 ft., IV' = 1 ft. 

Fig. 73 shows the scale (12 inches long) with which the 
student should be supplied, and the manner of using it. One 
edge is divided the whole length into inches and sixteenths of 
an inch, and is used for full-size drawings. The other edge 
contains two scales, namely, 1^ inches and 3 inches to the foot, 
indicated by the figures IJ and 3 at ^ and B. It will be 
noticed that on the scale of 3 inches to the foot the zero mark 
is at C instead of at (r, as in full-size scales. It is put there for 
convenience in reading feet and inches at the same time. The 
figures indicating the number of feet on this scale are placed 
along the extreme upper edge at D, E, and F. To lay off 2 feet 



10 



MECHANICAL DRAWING. 



CO* 

1 



*o 



f inches from some point, as H, towards another point, as /, 
place the scale on the point //, so that the 
2-foot mark will fall on this point ; then, from 
the zero mark, lay off 3f inches, as shown, 
locating the point /. HI will be 2 feet 3J 
inches long. The same remarks apply to the 
other scale of 1-J- inches to the foot. To draw 
to half size, or 6 inches to the foot, use the full- 
size scale, and remember that ever}^ \ inch on 
that scale corresponds to 1 inch on the object, 
that is, that every dimension is only half of the 
real length. To lay off 5|- inches, lay off 5 
half-inches and -^-^ of an inch over ; the result 
is a line b^ inches long to a scale of 6 inches to 
the foot. 

If it is desired to draw to a scale of f of an 
inch to the foot, or -^^ size, use the scale of 1^ 
inches to the foot, halving all dimensions, as 
in the previous case of drawing to a scale of 6 
inches to the foot with a full-size scale. It 
sometimes happens that a draftsman is obliged 
to make a scale, when the size of his plate is 
limited and a general drawing of some object is 
desired. By general drawing is meant a com- 
plete view of the object in plan, and also one or 
tw^o elevations. In such a case one scale ma}^ 
be too large to enable the drawing to be made 
on a sheet of the required size ; another scale 
may make it too small to show up Avell. For 
example, an \ scale may be too large, and a -^^ 
scale too small ; a -^^ scale ma}^ be just right. 
If the draftsman has no yV scale (that is, a 
scale of 1 inch to the foot), he may make one 
by taking a piece of heavy drawing paper and 
cutting out a strip about the size of an ordinary 
scale, and laying off the inch divisions on it. 
Each division or part will represent 1 foot on 
the object. Divide one of the end parts into 



MECHANICAL DRAWING. 11 



12 equal parts, and each will represent 1 inch on the object. 
Lines indicating half- and quarter-inches may be drawn, if 
considered necessar3^ 

Fig. 74 shows part of a scale made in this manner, giving 



l\2 & 



wmm\ 

6\ .y o\ 



Fig. 74. 



feet, inches, and half-inches — the quarters, eighths, etc. of an 
inch being judged by the eye. 



DRAWI]SG PLATE, TITLE: MACHI:N^E DETAILS. 

49. Fig. 1 shows a double square-tlireadecl screw 

3 inches in diameter and 1|- inches pitch, having a hexagonal 
head and nut. The screw is 10^ inches long, and the distance 
between the faces of the head and nut is 6f inches. The head 
and the nut are each 2^ inches long, are hexagonal in shape, and 
their long diameters are 5J inches. Since this screw is drawn 
full size, and is comparatively of large diameter, the true pro- 
jection of the helix is drawn instead of the conventional method 
used in Fig. 2 of the plate entitled Details. 

Draw the center line m n ; lay off A 3' equal to 6f inches, and 
through 3' draw CD perpendicular to mn. Make 3'E equal 
to 2^1 inches, and draw F G parallel to CD. Divide CZ), which 
is 5;^ inches long, into four equal parts, and through the points 
C,H,J, and D, draw lines C L, HI, JK and DM parallel to 
m n. With 3' as a center, and 3'E sls a radius, describe the 
arc IE K, intersecting HI and JK in / and K. Project the 
points land iTupon CL and DM, locating the points L and M, 
and pass through L and / and through K and M circular arcs 
tangent to FG. The centers of these arcs will lie on lines per- 
pendicular to the center line m7i, and midway between L and /, 
and between K and M. Therefore, draw NG parallel to the 
center line mn, through a point half the distance between JK 
and D M, and find by trial a point N at such a distance from G 



12 MECHANICAL DRAWING. 

that, with the radius N G, the arc will pass through K, G, and M. 
Draw the nut in the same manner. This is the conventional 
method of representing a nut. 

To construct the screw, draw through some convenient point 
a line QR parallel to CD. From as a center, describe 
two semicircles whose diameters are equal to the top and bottom 
diameters of the screw thread, intersecting the line QR in the 
points Q, q, r, and R. From these points draw lines to S, s, T, 
and t, parallel to the center line mn; evidently these lines 
coincide with the top and bottom of the screw^ thread. The 
depth of the thread is found as in Fig. 2 of the plate entitled 
Details. 

Divide the semicircles into any number of equal parts, in this 
case 6 ; this is best done by first dividing the exterior semicircle 
into the required number of parts, as Q, 1, 2, S, 4-, S, and R, and 
then drawing radii through each point from 0, which divides 
the interior semicircle similarly. Lay off on the line R t, or any 
other line, as U F, which is parallel to the center line m n, the 
pitch of the screw, or 1^ inches, and divide it into twice 
the number of equal parts that the semicircles have been divided 
into. 

Now, construct the helix 6 5 4^ 3 2 1 W, SiS described in Plate 
V, for the top diameter ; also the helix 6' 5' 4-' 3 X\ having the 
same pitch, for the bottom diameter.. As this is a double square- 
threaded screw, the widths, as well as the depths of the threads 
and grooves, are equal to \ of the pitch, or 1^ X i = f of an 
inch. (See Fig. 2, last plate. ) 

Consequently, to lay off the ^vidths of the threads and 
grooves, divide the pitch, or line V F, into four equal parts, as 
i, ^, ^, and C/, and through these points draw lines parallel to 
CD, intersecting the lines which represent the top and bottom 
diameters of the screw, in the points a, e, and Z' ; &, g^ and Z ; 
c^j\ and TF; d, X, and F; draw through these points other 
helical curves parallel to those already drawn. The remaining 
threads of the screw may be drawn in the same manner, but an 
easier and quicker method is to- cut a curve of the same shape 
as those already drawn, out of a piece of bristol board or card- 
board, and use it as a template. The manner of constructing 



MECHANICAL DRAWING. 13 



the curves X 1' 2' S' and 3 Jf! 5' 6' should be clearly evident 
from the drawing. The dotted curves need not be drawn by 
the student, as they are merely put in to show the connections 
betAveen the different threads. 

In Fig. 2 are shown a section and end view of a shaft flange 
coupling, used for connecting the ends of two shafts. In 
order not to take up too much room on the plate, the coupling 
is drawn to a reduced scale, which is marked on the drawing as 
3 inches = 1 foot. Using the scale of 3 inches = 1 foot (see 
Art. 48), draw the figure from the dimensions given, first draw- 
ing all of the sectional part, except the bolt. Then draw the 
end elevation as shown, and, lastly, the bolt in the sectional 
view. The part ABC is a key sunk into the shafts to keep 
them from turning within the coupling. The shafts them- 
selves are made of wrought iron, as indicated by the sectioning. 

Fig. 3 is a front and side elevation of a gland. This is also 
drawn to a scale of 3 inches = 1 foot, and should be constructed 
Avithout difficulty from the dimensions given. The line A^ 
marked 6f" r, means that the radius of the arc BAD is 6f 
inches long ; so, also, CB^ marked IJ" r, means that the radius 
of the arc B E is 1^ inches long. Since no dimensions are 
given for the other two arcs, it is understood that their radii are 
the same as for the first two. Whenever a dimension is given, 
like 0^, specifying the length of a radius, the letter r, or the 
abbreviation rad, should always be placed after it. . 

Fig. 4 shows a riveted joint, or two plates riveted together. 
The front elevation and a cross-section through one of the rivets 
are given. The diameter of the rivets is J inch, and the pitch 
(the distance betAveen the centers of two consecutive rivets) is 
1^ inches. These, and the other dimensions, are obtained from 
the drawing. DraAv the cross-section first, as shoAvn in the 
figure, and, after that, the elevation. The scale is full size. 

Fig. 5 shows a clamp, dog, or carrier, as it might be 
termed. It can be readily draAvn from the dimensions giA^en. 
It will be noticed that part of the pin A B is flattened. This is 
seen more clearly in the top view, shoAAm by the dotted lines. 
It is to be drawn to a scale of 3 inches = 1 foot. 

Fig. 6 shoAvs a clamii box to be attached to beams for 



14 MECHANICAL DRAWING. 



shafting to pass through. The scale to which it is drawn is 
half size, that is, 6 inches = 1 foot. The curves at A, B, etc. 
are not exact projections of the curve of intersection of the round 
and flat surfaces shown in the other view, but are drawn as 
circular arcs, from which they differ but little, and the time 
occupied in finding the different points on the curve is saved. 
This answers the purpose when making shop drawings, just 
as Avell as the exact method. The curve CFD is the projec- 
tion of the part D E F, shown by the dotted lines in the 
elevation, which is removed in order that the nut may be turned 
around. G is an oil hole. It will be noticed that the bolt 
holes are larger than the bolts ; this allows the clamp box a 
little play, should it be necessary. It also allows the holes to 
be cored in the box when the casting is made, instead of being 
drilled afterwards. On all drawings made for the shop, or on 
which dimensions are given or required, the scale should 
invariably be specified. If more than one scale is used, as in 
the last plate, where three different ones were used, it should ])e 
given for each figure. 



DRAWIIS^G PI.ATE, TITLE: BAXD-WHEEL. 

50. This plate shows an elevation and cross-section of one- 
half of a 14-foot band-^vlieel having eight arms. Draw both 
views at the same time, so that any part of the one view may 
be projected on to the other. 

Draw in the principal center lines first, and then draw in the 
rim and hub in both views. With a 45° triangle draw in the 
center lines of the arms in the elevation, and draw in the arms 
in both views. 

The cross-section shows that the wheel is crowned ; that is, it 
is turned larger at the center and slopes gradually to the edges. 
This prevents the belt from slipping off, and accounts for the 
double line representing the periphery of the wheel in the 
elevation. The part of the arm sectioned at A B indicates that 
a cross-section on A B would look like the cross-section shown, 
and that the arms are elliptical in shape. This method of 



MECHANICAL DFxAWING. 15 

showing the cross-section in cases of this kind is very com- 
monly used in drawing rooms. 

CD and CD' are kej^-ways for fastening the wheel to its 
shaft. The cross-sectional view shows that the hub is hollowed 
out. It was cored out thus when the wheel was cast, in order 
to save the time and expense of boring it through its whole 
length. This view, in connection with the dotted lines of the 
elevation, shows that the arms are hollow ; the cross-section on 
A B also shows it. The arms taper gradually from 7 inches at 
F to of inches at G, the same taper continuing on to H. The 
part E F has the same cross-section at every point, and, con- 
sequently, is straight. The core holes /, K^ L, etc. are 
reinforced ; that is, they have bosses on the inside to strengthen 
the arms where the holes are. It is necessary that these holes 
1)6 in every casting of this kind, so that the cores of the arms 
can be removed through them. The drawing can noAV be 
finished without further explanation. 



J>KA\MX(t PJ.ATE, title : ECCEXTRIC AXD 
BKAKE EEVER. 

51. Fig. 1 shows an elevation of an eccentric and its 

strap. The strap is made in two pieces, and l:)olted together 
with a small space ^V ^^ ^^^ i"^'^ wide between them. Locate 
the point 0, the center of the strap, and draw the center lines, 
A B, m ,u CC, and DD'. Make the offset 0' one-half of the 
throw of the eccentric, or, in this case, f inch, thus locating 
0', the center of the eccentric shaft. Construct the rest of the 
view from the dimensions given, noting that the arc E E' and 
F F' are concentric with 0, while G G' and H H' are concentric 
with 0'. The part F F' G'G is entirely open, and is made so in 
order to lighten the eccentric. 

Fig. 2 is a section of the eccentric and strap. The section 
is drawn in a conventional manner, it being all taken on the 
line A B, Fig. 1, except that part of the eccentric between G' 
and F', wdiere, instead of sectioning, the drawing shows it open 
from L to P, Fig. 2, as if the section had been taken on the line 



16 MECHANICAL DRAWING. 



J. This attracts attention to the open part of the eccentric, 
and shows it more clearly. 

It will be noticed that the slope of the threads in the sec- 
tional part is the same as for the left-handed screw. The 
thread, however, is right-handed, and the reason for showing it 
in this manner is that it is the bottom of the thread that is 
being looked at ; that is, the section of a right-handed nut and 
the projection of the bottom of a right-handed screw are the 
same as the projection of the top of a left-handed screw. It 
will also be noticed that the sectional lines on the eccentric 
run in opposite directions to those on the strap. This is 
always done wdien two different pieces meet, and serves to 
indicate that they are separate pieces. Each piece should be 
sectioned entirely in the same direction, no matter if there is a 
break, as in the present case, between L and P. This shows 
that A B CDE is one piece. The dotted hole atZ, Fig. 1, is an 
oil hole. 

Fig. 3 shows a "brake leA'er drawn to a scale of 3 inches = 

1 foot. Owing to its length being too great to be shown 
entirely on the drawing to this scale, the handle is shown as if 
a piece had been broken out, the dimension line, 4 feet 7 inches, 
giving the distance between the two centers and 0'. The 
lever should be readily drawn from the dimensions given. 
To proportion it properly, where the size of the paper does not 
permit the whole of it to be drawn, proceed as follows : The 
length between the centers is 4 feet 7 inches = 55 inches. 
The wddth through 0' is 2J inches, and through 4 inches. 
Hence, 4" — 2 J" = If" ; 1. 75" == the taper in 55 inches. Meas- 
ure o& OA = say, 2 feet. The width at A may be found as 

follows: -4^- = taper in 1 inch. ^-^ X 24 = .76 inch, 

00 DO 

nearly, the taper in 2 feet. 4" — .76" = 3.24" = B C, or the 
width at A. Now locate the point 0', and from it as a center 
describe a curve 2J inches in diameter. Draw lines tangent to 
this curve, and parallel to the edges between A and already 
found. 

It should be noticed that the center of the brake lever in the 
left-hand view is not situated at the joint where the two parts 



MECHANICAL DRAWING. 



17 



come together, but coincides with the center of the handle, as 
it should do. 

52. Fig. 75 shows the ordinary conventional method of 
representing a nut. The bottom of the thread is IJ inches in 
diameter, and is represented by the dotted circle ; this shows 
that it is intended for a scrcAv 1|- inches in diameter. The 
height of the nut equals the diameter of the bolt or screw on 
which the thread is cut. Tlie two views on the center line m n 
should be drawn without difficulty. To draw the curves ea 
and ad, project b and.c at right angles to t v in the points 
d, a, and e ; pass arcs of circles through e and a, and through 




I i / oT i i 






r"^ 



n 



Fig. 75. 

d and a tangent to /(/, finding the centers of these arcs by 
trial. The best way of doing this is to draw lines parallel to 
t V midway between e and a and between a and d. Then, by 
trial with the compasses, find a center on these lines such that 
an arc struck with the compasses from this center will pass 
through e and a (or a and d) and be tangent to fg. In the 
right-hand view, the radius of the arc he is the same as the 
height of the nut ; the centers of the other two arcs are found 
by trial in the manner just described. 



18 MECHANICAL DRA^yING. 

r>llAWi:N^G PIRATE, TITTLE: E:NG1XEER1XG 
DETAIES. 

53. Fig. 1 shows a top view and elevation in partial section 
of a coniiectmg*-rod.. Draw the center lines m n and m' n' ; 
lay off on one of them the length of the rod between the centers 
(4 feet Scinches), and through the two points just located draw 
the vertical center lines tv and t' v' . The two views should be 
easily drawn from the dimensions given. It will be noticed by 
the sectioning that the boxes are made of brass, lined with 
babbitt metal. The bolt in the crank end of the rod is marked, 
"Taper of Pin -^^ of an inch per foot." To draw it, locate its 
center line, and lay off under the head its diameter, 2 inches. 
Measure off on the center line from the head downwards 12 
inches, and lay off at this point a line representing a diameter 
of lyf inches. Join by straight lines the ends of the two lines 
just drawn, and they will form the edges of the pin. 

Fig. 2 shows an expansion-joint. It is placed near the 
middle of a long line of steam pipes to alloAv for the expansion 
and contraction of the pipes, owing to the great changes of tem- 
perature. A is the gland for the stuffing-box C, which forms 
part of the body B^ to which it is fastened by studs not shown 
in the drawing, but which pass through holes in the flanges of 
A and B. Packing is placed in the stuffing-box, making a 
steam-tight arrangement. The sliding tube marked D is made 
of cast iron, partly covered with a thin cylinder of brass called 
a sleeve. The gland A and that part of B through which D 
passes are lined, or bnsliecl, with brass. ' This is done to keep 
the surfaces that slide over each other from rusting by the action 
of the steam and sticking together, as would be the case if they 
were iron. The tube D is bolted to one section of the pipe, the 
other section of the pipe being bolted to the other end of 
the body B. The rods £", E act merely as guides. When the 
whole is in j^osition, the two nuts at F, F will not touch the 
flange, but will be at a little distance from it ; the gland of 
the stuffing-box Avill also be about half-way in. ^^'hen the 
pipe is heated it expands, and the two ends at D and B tend to 
come together ; the brass part D slides through its stuffing-box ; 



MECHANICAL DRAWING. 19 



the distance between the end ^and the edge G decreases, and 
the distance between the nuts F and the flange increases. 
When the pipe is cooled it contracts ; the distance between H 
and G increases, and between the nuts F and the flange it 
decreases. The student should be able to draw the figure from 
the dimensions given. 



DRAWIXG PLATE, TITLE: REVERSllSG LEVER. 

54. This plate shows a drawing of a reversing; lever, 
together with its stand, which is suitable for a brake lever on 
hoisting engines. To draw it, first draw the center line m n, the 
base line A B, and the base and bosses in the side elevation. 
Locate the center on m n, 9 inches below A B. With as a 
center, and a radius equal to 2 feet 3 inches, describe an arc of 
a circle. On each side of m n lay off 12 inches, and draw ver- 
tical lines through the points ; these lines intersect the arc just 
described in 0', 0', the centers of the pins. The arc intersects 
mn in P ; hence, lay off 1 inch on each side of P, along mw, 
and draw arcs of circles through these points ; they will be the 
limiting lines of the top and bottom of the wrought-iron sector. 
With the two centers 0' and* a radius of 1 inch, describe the two 
circles as shown. Set the spacing dividers to 1 inch, and step 
off the teeth on the outer circular arc. Draw all the short 
shaded lines, as a b, radial ; that is, if a line be drawn from the 
point a to the center 0, the point b will fall on this line. 
Measure, from the base line upwards, C D ^ 1^ inches and, 
with a center on m n and a radius equal to 10 inches, pass an 
arc through the point D ; also one through E^ half an inch 
beloAV D, using the same center. With a radius equal to 18 
inches, find by trial the center Q, which is so located that an 
arc described with this point as a center, with a radius 18 
inches long, will be tangent to the arc just passed through D, 
and to the circle described about 0' . With the same center, 
and a radius J of an inch longer, describe the other arc tangent 
to the arc through E. Noav draw a faint pencil line on each 
side of, and parallel to, m n, and distant 5f inches from it. 
With B as a center, and a 3-inch radius, describe an arc tangent 



20 MECHANICAL DRAWING. 



to the perpendicular just drawn, and to the upper edge of the 
base. Find by trial the center Q', such that an arc described 
with Q' as a center, and a radius equal to 19f -^ ^ = 19| inches, 
will be tangent to the arc just drawn and to the circle whose 
center is 0'. With the same center, and a radius equal to 19f 
inches, describe another arc tangent to an arc described with R 
as a center and a radius equal to 3 J inches. The construction 
is the same for each side of m n. 

The remainder of this view can be easily drawn from the 
dimensions given. The dotted part between C and is a rib ; 
it is shown more clearly in the front elevation, in which F G is 
its outer edge. The line cde on the top of the lever indicates a 
flat surface. In the front elevation the line HI represents the 
line described with the 19f-inch and Scinch radii, and the line 
H' T rejDresents the line described with the 18- inch and 10- inch 
radii. Theoretically, the entire rib FGKL should be sec- 
tioned, and the outline of the sectional part between N' and N 
should be dotted, but, for convenience, a conventional method 
is used. The thickness, f inch, of the sectional part, is the 
thickness of all that part of the arm below the base, except that 
included between the dotted lines on the side elevation. The 
dotted line RS'is the projection of the edge R' S' . 



DRAWING PI.ATE, TITI.E : 5-IXCH GLOBE VAEVE. 

55. On this plate is shown a longitudinal section of a 
5-iiieli g'lobe Talve. Draw the center lines m a and p q. 
Draw the faces of the flanges A A' and B B', Tf inches from the 
center line m n, and construct the flanges according to 
the dimensions given. Locate P on mn 6 inches below p q, and 
with a center on m n, and a radius of 6|^ + f = 7|- inches, 
describe the arc CF C. ^\^ith the same center, and a radius 
6^ inches long, describe the arc C C. With a center on the 
inside edge E E' of the flange, and a radius equal to 2 inches, 
describe the arc CD tangent to C C. With the same center, 
describe the arc CD' tangent to C'C, and draw D' D" straight. 
With a radius equal to ^ of an inch, describe the fillet D E, 
tangent to i) Cand EE'. FF and F'F' are both struck with 



MECHANICAL DRAWING. 21 



the same radius as CP C, and no difficulty should be expe- 
rienced in drawing the upper part of the body. 

The valve is made of brass, as shoAvn by the method of 
sectioning. The seat H is flat, in order to obtain a better fit, 
and save time in grinding ; it makes an angle of 45° with jjq. 
The lower end of the valve stem, used to raise the valve by 
turning the hand-wheel on the upper end, is curved to a radius 
of 4:\^ inches, having a center 0. 

The lower edge of the sectioned part of the valve is struck 
with a radius having the same center. The screw is a single 
square thread, having 3 threads per inch, and the nut is square. 
It is made of brass, and inserted through a hole cored in the 
boss on the bottom of the upper casting or bonnet. The screw 
is then screwed in, and the hand- wheel put on the upper end, 
which is made square. The bonnet is then placed upon the 
body of the valve, and bolted down, as shown. There is also a 
stuffing-box in the bonnet, as shown, to prevent leakage. It 
will be noticed that the section of the hand- wheel is in all 
respects similar to the one shown in the plate entitled Details. 



DRAWI:N^G plate, title : SHAFT HAXGER. 

56. This plate shows a drawing of a liang-er used to sup- 
port shafting. There are shown a side view, half in elevation 
and half in section on the line FZ, part of a top view, part of a 
bottom view, a complete longitudinal section on the center line 
m n at right angles to the plane of the paper, and two small 
sections through the frame. For convenience in describing, the 
different view^s will be numbered. 

Draw Fig. 1 first, which shows a half elevation and a half 
section. No great difficulty should be experienced in drawing 
it. It will be noticed that the journal-box through which the 
shaft passes has a spherical bearing ; this is shown by the fact 
that the radius of the curve is the same, or 1-| inches, in Fig. 1 
and Fig. 2, the latter being a view at right angles to Fig. 1. The 
object to be attained by making the bearing partly spherical is 
to provide for self-adjustment in any direction, in case the 
shaft is not perfectly straight. 



22 MECHANICAL DRAWING. 



Fig. 2 shows very plainly how the shaft may be adjusted 
vertically. The set-screws A, A are released, and the large 
screws B and B' are screwed up or down, according as the 
shaft is to be raised or lowered, the spherical bearing allowing 
of adjustment at every point. The set-screws are then screwed 
down or set, so as to prevent B and B' from changing their 
positions. It will be noticed that the journal-box is made in 
two parts. Fig. 2 is a section on a line mn, and shows the 
whole length of the hanger. The part sectioned at E and E is 
shown in Figs. 1 and 4 by EE. The dotted lines between 
them show the projection of the boss drawn at E, in Figs. 1 
and 4, but not seen in this view. The lines forming the outline 
EDE'E show the projections of the hanger frame. The screws 
B and B' are made 'hollow, to lighten them. The dotted ellipse 
in B is the projection of the rib shown at L in Fig. 1. 

Fig. 3 is a bottom view as far as the line C C, after the oil 
pan and screw^ B' have been removed. D is the projection of 
the boss D in Figs. 1 and 2, through which the set-screw A 
passes. 

Fig. 4 is a partial top view. This can be drawn from the 
dimensions given, without any special instructions. 

Fig. 5 is a section through CD, Fig. 1, and G H, Fig. 2. It 
shows the shape of the frame, which is also shown by the dotted 
outline P, in Fig. 4. This section is drawn more particularly 
to show that the radius of the curve on each side of any section 
of the vertical part of the frame is the same. 

Fig. 6 is a section through A B, Fig. 4, and //v, Fig. 1. 



TITI^E : BEIS^CH TISE. 

5T. This plate shows a beneli vise and its details. 

A drawing of this kind is called a detail draAving*. Fig. 1 is 
a complete top view, and Fig. 2 is a section through the center 
line CD. The remaining figures are drawings of the different 
parts, or details. The actual practice in the drawing-room 
would be to draw Figs. 1 and 2 first, and then the details, 
but in the present case the student will do well to draw the 
details first, as it will help him in drawing the other two views, 



MECHANICAL DRAWING. • 23 



]3articularly since nearly all of the dimensions are given on the 
details. Following out this plan, leave space for Figs. 1 and 2, 
and begin by draAving Fig. 8. This consists of three views of 
the jaw, the part marked A in Figs. 1 and 2. The parts marked 
B, (7, and D, in Figs. 1, 2, and 3, are circular in shape, so as to 
j)ermit the back jaw A of the vise to swing when the pin E is 
removed. This allows the vise to hold tapered pieces with as 
much firmness as straight ones. 

Fig. 4 is a detail, with dimensions, of the pin E. 

Fig. 5 is a detail of that part of the vise marked F in Figs. 1 
and 2, and also of the wrought-iron nut G. The reason that 
only a part of the nut G is sectioned in Fig. 2 is that a con- 
ventional method has been used. In reality, the whole of the 
nut should be sectioned. It would be impossible to take a 
section of the nut in the manner shown. 

Figs. 6 shows a top view, longitudinal section, and cross- 
section of the front jaw. This is cored out to admit the screw 
and the nut. The form of the cored part is shoAvn by the 
longitudinal section and cross-section through E F and A B. 
The front jaw moves in and out with the screw, as shown by 
Fig. 2, the collar L being held in place by the small set-screw. 
This is sufficient, since there is no stress on the collar beyond 
the force required to pull the jaw outwards, the force exerted 
by screwing the jaws together coming entirel}^ on the surface M 
of the screw head. 

A separate detail drawing of the screw is not required, since 
all the dimensions are given in Fig. 2. Figs. 1 and 2 can now be 
drawn, the necessary dimensions being obtained from the details. 

For ordinary shop drawings, the details are usually drawn to 
a larger scale than the general drawings, Figs. 1 and 2. In this 
case the size of the plate would not permit an enlargement. 



DRAWIISG PLATE, TITLE: PROFILES OF GEAR- 
TEETH. 

58. If a circle be rolled on a straight line without sliding, 
a point on the circumference of the circle will describe a curve 
called the cycloid. The circle is called the generating 



24 MECHANICAL DRAWING. 



circle. The shape of the curve and the manner of drawing it 
are shoAvn in Fig. 1. Let be the center of the generating 
circle, which is If inches in diameter, P the point on the cir- 
cumference of the generating circle, and A B the straight line 
on which the generating circle is rolled, and which is equal in 
length to the circumference of the generating circle, or If X 
3.1416 = 5.4978, say 5^ inches. The generating circle should 
be so placed that its center lies over the center of the line 
A B, as shown. Divide the generating circle into any number 
of equal parts, in this case 12, or PI, 1-2, 2-3, 3-4-, etc., and 
through these points draw lines CD, EF, G H, etc. parallel to 
the line AB. Through the center of the generating circle 
draw the radius 6. Divide each half of the line AB into 
half the number of equal parts that the generating circle is 
divided into, as Al, 1-2, 2-3, etc., and through these points 
draAV lines perpendicular to A B, terminating in the line G H, 
as A G, 1-1' , 2-2' , 3-3' , etc. From the point 1' , with a radius 
equal to the radius of the generating circle, as 0^ or I'-l, 
describe an arc intersecting the line KL in the point P^ ; from 
the point 2' , with the same radius, intersect the line //in the 
point P^ ; from the point 3' , with the same radius, intersect the 
line GH; continue in a similar manner with the remaining 
points 4' , 5' , 7', 8' , etc., intersecting the lines EF and CD in 
the points P^ P\ P\ P\ etc. The points A, P\ P\ P\ etc. are 
points in the curve through which the cycloid may be draw-n. 
It will be noticed that when the center of the generating 
circle coincides with the point G, the point P on the circum- 
ference of the generating circle coincides with the point A ; and 
that wdien the generating circle is revolved towards the right, 
without sliding, until the center coincides with the point 1' , 
the point P will coincide with the point P\ Thus it is seen 
how the point P passes through all the points from A to B, 
namely, A, P^, P^, P^, etc., when started at A and revolved 
towards the right to B. 

59. If the generating circle be rolled, without sliding, on the 
outside of the circumference of an arc of a circle supposed to be 
at rest, instead of being rolled on a straight line, the curve 



MECHANICAL DRAWING. 25 



described by a point P of the generating circle will be an 
epicycloid. 

The manner of drawing such a curve is shoAvn in Fig. 2. 
A B is the arc upon which the generating circle is rolled, its 
center being at aS', and its radius being 3^ inches. The diameter 
of the generating circle is in this case the same as in Fig. 1, or 
If inches. Make the lengths of the arcs 6 A and 6 B equal to 
half the length of the circumference of the generating circle, by 
first calculating the length of half the circumference of the gen- 
erating circle, and drawing a straight line tangent to the arc 
A6 B at 6^ and making it equal in length to half the circum- 
ference of the generating circle. Then make the arc 6 A equal 
to this line by means of the approximate method given in 
problem 20, Art. 33. Divide the arc A6 B and also the gen- 
erating circle into the same number of equal parts, in this case 
12, as Al, 1-2^ 2-3, etc., and Pi, 1-2, 2-8, etc., and draw radii 
from the center S to the points of division on the arc A6 B. 
During the revolution of the generating circle, the center Avill 
describe an arc m n concentric with the arc A6 B, and having 
the same number of degrees in it as A 6 B. Produce the radii 
just drawn to the arc of center positions m n, intersecting this 
arc in the points m, i', ^', 3', 4', etc. Through the points of 
equal divisions, 1, 2, 3, etc., of the generating circle, pass con- 
centric arcs having the center S, as CD, EF, G H, IJ, and KL. 
With the points 1' , 2', 8', J/! , etc. as centers, and radii equal to 
the radius of the generating circle, describe arcs cutting the arcs 
KL, IJ, G H, etc., in the points P\ P'\ P^, etc., which are points 
on the epicycloid. 

60. When the generating circle rolls on the inside of the 
arc, the curve described by a point on the circumference is 
called a liypocycloicl. The method of drawing it is similar 
in all resj^ects to that just given for the epicycloid. The 
student should be able to construct it from the drawing without 
further explanation. The diameter of the generating circle is 
If inches, as before. 

61. Suppose that a string is wound upon a cylinder, and 
that the end of the string is at the point P, in Fig. 3. If this 



26 MECHANICAL DRAWING. 



string be unwound from the cylinder, keeping it constantly 
tight, the end P will describe a curve known as the involute 
of tlie circle, or, more simply, the involute. To construct it 
geometrically, let O be the center of the given circle represent- 
ing the cylinder, which, in Fig. 3, is 2\ inches in diameter, and 
P the free end of the string when wound upon the cylinder. 
Divide one-half of the given circle representing the cylinder 
into any number of equal parts, in this case 6, as Pi, 1-2, 2-3, 
etc., and through each of these points draw tangents to the circle, 
as P\ P^, P^, etc. To draw these tangents, first draw the radii 
01, 02, 05, etc., and then draw the tangents 1P\2P\3P\ 
etc. at right angles to them. By means of the approximate 
method given in problem 21, Art. 33, find the length of the 
arc IP, and make the length of the tangent 1 P^ equal to this 
length ; of the tangent 2 P'\ equal to twice this length ; of the 
tangent 3 P^, equal to three times this length, and so on. The 
curve drawn through the points P\ P\ P^, P*, etc. will be the 
required involute. The use of these curves Avill now be 
explained : 

62. On the plate entitled Spur Gear- Wheels, Fig. 1, is 
shown one-half of two spur gear- wheels in mesh. The two 
dotted circles tangent to each other at P are concentric to the 
centers of the gear-wheels, and are called the pitch, circles. 
The diameter of any gear-wheel is always understood to be the 
diameter of its pitch circle unless it is specified as diameter 
at root, or diameter over all. The length of that part of 
the pitch circle between the centers of an}^ two consecutive 
teeth is called the circular pitcli, or simply the pitcli. 
Thus, in the last-mentioned figure, the length of the arc ab is 
equal to the pitch of either gear-wheel. When the gear-wheels 
are cut in a gear-cutter, the width of the tooth c d on the pitch 
line is equal to the space df ; that is, the arc c d is equal to the 
arc df, and each is equal to half the pitch. When the gear- 
wheels are cast, that is, when they are not cut in a gear- cutter, 
clearance is given between the back of one tooth and the front 
of the tooth following, to allow for inequahties in casting. This 
clearance, or back lasli, as it is usually termed, is generally 



MECHANICAL DRAWING. 27 



made equal to 4?c of the pitch. This is done by making tlie 
thickness of the teeth ccZ equal to .48 of the pitch. 

The part C C^ of the tooth which lies beyond the pitch circle 
is called the addendum, and the part C C^ which lies below it 
is called the root. The face of the tooth is the part CC^ C'C, 
Fig. 2, of the tooth al)ove the pitch circle, extending the whole 
width of the tooth. The flank is the part CC,C"C, Fig. 2, 
of the tooth beloAV the pitch circle, extending the whole width 
of the tooth. The terms addendum and root mean distances 
only, while face and flank mean surfaces. 

The usual practice is to make the addendum equal to .3/*, 
and the root equal to .4 P. P = the circular pitch. The dis- 
tance Cj C, is called the whole depth of the tooth. The method 
of describing the curves of teeth shown on the plate entitled 
Profiles of Gear-Teeth, Fig. 4, is a convenient way of drawing 
the cycloidal, or double-curved teeth. Cycloidal teeth 
are constructed by making the outline of the face a part of an 
epicycloid, and the flanks a part of the hypocycloid ; hence the 
name — double-curved teeth. 

63. In Fig. 4 of the lAate entitled Profiles of Gear- Teeth, 
let AB he part of a pitch circle struck with a radius of, say, 5^ 
inches. For convenience in drawing the tooth, let the pitch be 2 
inches. With as a center, Avhich is the center of the gear-wheel, 
and a radius equal to 5^ inches, describe the arc A B, part of the 
pitch circle. Through draw a straight line S, cutting A B in 
P. Take the radius of the generating circles S P and >S" P, equal 
to 1|^ inches for this case, and describe arcs having centers at S 
and aS" on the line S. With as center and S as radius, 
describe the arc S.,S^. In connection with gear-wheel teeth, 
the generating circles are frequently called describing; circles. 
Roll the outer describing circle upon A B in such a manner 
that the center S will move in the direction of the arrow along 
the arc S.^S^. By means of the method given in Fig. 2, find 
the points P\ P\ P^ etc. on the epicycloid described by the 
point P. Trace a faint curve through the points just found, 
and measure off on the pitch circle the thickness of the tooth. 
PD = .48 2^ = .48 X 2" = .96". 
Make EF= the addendum = .3 X p =-- .S X 2" = .6". 



28 MECHANICAL DRAWING. 



With as a center and OF as a radius, descril)e an arc cut- 
ting the epicycloid in G. Now roll the inner describing circle 
on A B, so that its center aS" moves in the direction of the 
arrow, and find the points P^, P.^, P^, etc. of the hypocycloid 
described by the point P, through which trace a faint curve. 
Make EF' equal the flank of the tooth =r. Ap=Ax2" = .8", 
and with as a center and F' as a radius, describe an arc 
cutting the hypocycloid in G' . P G' is the outline of the flank 
of the tooth, and P G that of the face. Since it would be a 
tedious operation to draw all the tooth curves in this manner, 
it is usual to approximate the curves by means of circular arcs ; 
that is, to find, by trial, a center Q, and a radius Q P, such that 
an arc described from this center, and with this radius, will 
pass through the points on the curve G P, and coincide with 
that curve as closely as possible ; also, to do the same with 
regard to the curve P G', using the center Q' and the radius 
Q' P. To find the center Q or Q' of these circular arcs proceed 
as follow^s : With P and G as centers and any radius, describe 
arcs intersecting in C and C. Draw a straight line through C 
and C ; the center Q must line on C C to the left of G P. Try 
different points i, 2, 3, 4, etc. on this line as centers, and 1 G, 
2 (t, etc. as radii, and see if one of the arcs struck with either 
one of these centers and radii will coincide with the epicycloidal 
curve GP. Make this circular arc fit the curve for a short 
distance beyond G — as far as P^, for example ; this will ensure 
the arc being more nearly correct. This should be done in 
every case when finding an approximate radius of this kind. 
Continue in this manner until the point Q is found, such that 
an arc struck Avith Q as a center and Q G or Q P as a radius 
will coincide as closely as possible with G P. If a circle were 
drawn with as a center and Q as a radius, the centers of all 
the circular arcs of the faces of the teeth would lie in this circle, 
and the radii of these arcs would be equal in length to Q P. 
Hence, to find the center Q^ of the arc D H forming the back of 
the tooth, take D as a center and Q P as a radius, and describe 
a short arc cutting, in Q^ , the circle passing through Q. Then, 
with Q^ as a center and the same radius, describe the arc D H. 
In a similar manner, find the center Q' and describe P (r', also 



MECHANICAL DRAWING. 29 



DH'. Instead of letting the flank form a sharp corner at the 
l)ottom of the tooth, as shown dotted at G\ it is usual to put a 
small fillet there, as shown by the full line. This makes the 
tooth stronger and less liable to break or to crack in casting. 
The entire tooth outHne or curve G P G' or HD H' is called the 
profile of the tooth. 

64. A rack is a gear-wheel whose pitch circle is a straight 
line; the tops of tha teeth all lie in the same plane. A 
portion of a rack and one tooth are shown in Fig. 5. Take the 
pitch the same as before, then the addendum and root are also 
the same, that is, .6 of an inch and .8 of an inch. Take the 
radius of the describing circles If inches, as before. It is 
evident that the tooth profile will be formed of parts of cycloids, 
formed by rolling the describing (generating) circle upon the 
pitch line A B. Draw a small part of the cycloidal curves, as 
shown in the figure, by the method given in Fig. 1 ; lay off the 
addendum and root, and find the approximate radius in the 
same manner as in the last figure. The centers of the curves 
for the faces and flanks of all the teeth of the rack will evi- 
dently line on the straight lines passing through Q and Q', 
respectively, and parallel to the pitch line A B. 

65. In Fig. 6 is shown the manner of drawing the invo- 
lute, or single-curve tootli. The profile in this case is 
formed of a portion of an involute curve and a portion of the 
radius of the pitch circle. The circle from which the involute 
is constructed is called, in this case, the base circle. To find 
it, draw the pitch circle, of which the arc ^ i? is a part, with a 
radius equal to o-J- inches, and having its center at 0. Draw 
any radius. TF, cutting the arc A B in D. Through D draw 
the straight line E F^ making an angle of 75° with W. With 
as a center and a radius to be found by trial, draw a circle 
tangent to E F. This circle, of which the arc H G is a part, is 
the base circle, and cuts W in P. Upon this circle construct, 
in exactly the same manner as was shown in Fig. 3, a portion of 
an involute curve, passing through P. Lay oft' the addendum 
IK ^=- .6 of an inch, and, with as a center and /as a radius, 



30 MECHANICAL DRAWING. 

describe an arc to form the top of the tooth, intersecting the 
involute in L. That part of the flank below the base circle is 
straight, and is a part of the radius drawn to the point P. K I' 
is the root. The tooth has a fillet at L' and R', as in cycloidal 
teeth. A circular arc is passed through the points L and P, 
coinciding as nearh?- as possible with the involute curve LP. 
Its center Q is found in the same manner as in Fig. 4. For 
involute teeth it is only necessary to find the one center Q ; the 
centers for all the remaining teeth lie on a circle having as a 
center, and passing through Q. To draw the other side of the 
tooth, lay off on the pitch circle MN= .96 inch, as before. 
With M as a center and QN = Q P as a radius, draw an arc 
cutting, at Q^ , the circle passing through Q ; with Q^ as a center, 
and the same radius, describe the part P' R of the tooth profile 
above the base circle. The part P' R' below the base circle is a 
part of the radius OP'. 

In drawing any of the curves previously described, the 
greater the number of parts into which the describing or base 
circles are divided the greater will be the accuracy obtained. 
The profile of the rack tooth used for involute gears is a straight 
line making an angle of 15° with a line drawn perpendicular to 
the pitch line. Its construction is shown in Fig. 7. 



DEFiis^iTio^s^s a:n^d cai.cui.atio:n^s. 

QQ, When a revolving shaft transmits motion to another 
shaft parallel to it by means of gear- or tooth- wheels, in such a 
manner that two corresponding points, one on each gear-wheel, 
always lie in the same plane, the two gears are called spur 
gear-^vheels. When the shafts are not parallel, but their 
axes intersect in a point, as in the plate entitled Bevel Gears, 
they are called bevel gear-wheels. If two bevel gear-wheels 
which work together have pitch diameters of the same size, they 
are called miter gear-Avlieels. From what has preceded, it 
is evident that the circular pitch multiplied by the number of teeth 
equals the circumference of the pitch circle. 



MECHANICAL DRAWING. 31 

Let ft = circular pitch of gear-wheel ; 

n = numl^er of teeth ; 
d = pitch diameter ; 
TT = 3.1416 (~ is pronounced pi). 

Then, ^^^4^-' (!•) 

or, the diameter of the pitch circle equals the circular pitch multiplied 
by the number of teeth divided by 3.1Ifl6. 

V^% (2.) 

or, the circular pitch ecpicds the pitch diameter multiplied by 3.1Jf.l6 
divided by the number of teeth. 

or, the number of teeth equals the pitch diameter multiplied by 3.14-16 
divided by the circular pitch. 

AVhen constructing cycloidal teeth for gear-wheels, the diam- 
eters of the describing circles are usually made equal to one-half 
the diameter of the pitch circle of a gear-wheel having 12 teeth, 
of the same pitch as those of the gear-wdieel about to be made. 

Let (/' be the diameter of the describing circle ; then. 



V = -^ X i or d' = -^. (4.) 



Addendum = .3_p ; root = .4|> ; thickness of teeth for cast 
gears = .48 p, and for cut gears \ p. 



DRAWIiSG PI.ATE, TITJLE : SPUR GEAR-WPIEEI.S. 

67. This plate shows the halves of two cast gear-w^lieels, 

having cycloidal teeth, which work together, a cross-section of 
each gear being also given. The drawing is full size, the wheels 
not being show^n entire for want of room ; to have done so it 
would have been necessary to make the drawing to a reduced 
scale. The pitch is 1 incli, the number of teeth in the large 



32 MECHANICAL DRAWING. 



gear is 36, and in the small one 18. The pitch diameter of the 
large wheel is found by formula 1 to be 

d = i^T-j^Tr. = 11.46 inches, nearly. 
d.l41b 

The pitch diameter of the small gear = ^ = 5. 73 inches, 

nearly. 

The diameter of the describing circle is found by formula 4 

6x1 
to be d' = ^ ^ ,,^ = 1.91 inches. 
3.1416 

For all practical purposes, the diameter of the describing 
circle may be taken to the nearest 16th of an inch. For 
circular pitches under J inch, approximate the diameter of the 
describing circle to the nearest 32d of an inch. To find 
the nearest 16th or 32d, multiply the decimal part of the 
diameter by 16 or 32, and take the nearest whole number of 
the product as the number of 16ths or 32ds that the decimal 
represents. Thus, in the above, the decimal part of the 
diameter is .91 inch ; ,91 X 16 = 14.56. The nearest whole 
number to 14.56 is 15 ; hence, the diameter of the describing 
circle is 1^ inches. If the diameter had been required to 
the nearest 32d, .91 X 32 ^ 29.12 ; 29 is the nearest whole 
number ; hence, the diameter would be Iff inches. In this 
case, take the diameter as l^f inches, approximating to the 
nearest 16th for all circular pitches above ^ of an inch. 
The addendum will be .3 X 1 inch ^ .3 of an inch, the root = 
.4 X 1 inch = .4 of an inch, and the thickness of the tooth on 
the pitch circle = .48 X 1 inch = .48 of an inch. 

Draw the line of centers 0' between the two axes. With 
as a center describe a semicircle having a diameter of 11.46 
inches, cutting 0' in P. With 0' as a center, describe a semi- 
circle having a diameter of 5. 73 inches which shall be tangent to 
the first circle ; this semicircle also cuts 0' in P. These are the 

pitch circles. Divide the larger pitch circle into -^, or 18 equal 

parts, by using the protractor. This is accomplished by laying 
the protractor on the drawing in such a manner that the center 
of the protractor coincides with the center of the gear-wheel, 



MECHANICAL DRAWING. 33 

and then laying off on the drawing 18 divisions, each eqnal to 

10 degrees. The reason for this will l)e clear when it is 

360° 
rememhered that there are 360° in a circle, or ^ = 180° in 

a semicircle, and as there are 18 teeth in the semicircle, 180°^ 
18 ^= 10°, which is the angle between two lines drawn from the 
centers of any two consecutive teeth to the center 0. In a like 
manner, any circle may be divided into parts by using the pro- 
tractor. Make C C^ = .3 inch = addendum, and CC.^= A 
inch = root. AVith as a center, and C^ and C, as radii, 
describe light circles, called adclendviiii and root circles, to 
represent the tops and bottoms of the teeth. Consider the points 
of division just laid off on the pitch circle as the centers of the 
teeth, and lay off on each side one-half of the thickness cd of 
the tooth, or .48 X i^ = .24 inch. Upon another sheet of paper, 
strike a short arc of the pitch circle, and construct the profile 
of the tooth as described in the plate entitled Profiles of Gear- 
Teeth, using describing circles 1-^f inches in diameter. Having 
found the centers Q and Q^ of the circular arcs used for the pro- 
files of the teeth, draw circular arcs through these centers, as 
previously described ; then, wdth (see plate entitled Spur 
Gear- Wheels) as a center, and the same radii, describe circles ; 
these circles will contain the centers of the circular arcs w^hich 
form the teeth profiles. With the point ^ as a center, and a 
radius equal to the radius of the face of the tooth (found on the 
other sheet of paper before mentioned), describe an arc inter- 
secting the circle of face centers at Q. With Q as a center, and 
the same radius, describe the arc A D for the face of the tooth, 
the point D being the point of intersection of ^ Z> with the 
addendum circle. In the same way, draw the remaining faces of 
the teeth. To draw the flanks, take a point representing the 
intersection of a tooth profile with the pitch circle (the point B^ 
for example) as a center, and a radius equal to the radius of the 
flank found on the other paper on which the tooth profile was 
drawn, and describe an arc intersecting the circle of the flank 
centers in Q^. With Q^ as a center, and the same radius, 
describe the flank curve, stopping at the root circle. Draw the 
flanks of the remaining teeth in the same way, and then put in 



34 MECHANICAL DRAWING. 

the fillets. The remaining part of Fig. 1 can be easily drawn 
from the dimensions given. 

Fig. 2 is a conventional method of drawing cross-sections of 
gears. The hubs and rims are sectioned, but the teeth and 
arms are not. This is similar to the wheel shown on the plate 
entitled Details. This method of sectioning makes the views 
clearer, and saves the time spent in sectioning. 

In Fig. 3 the entire gear is sectioned except the teeth. The 
student should now be able to finish the plate without further 
instructions. 



DRAWIIS^G PLATE, TITLE : BEVEL-GEARS. 

68. To draw in section and projection two cast bevel- 
gears whose axes intersect at right angles : The number of 
teeth in the large gear is 20 ; in the pinion 16. The circular 
pitch is 1 inch ; the teeth are to be of the cycloidal form, 
having a face 2 inches wide. In any kind of gearing, whether 
spur, bevel, or spiral, the smaller wheel is called the pinion. 

Calculate the pitch diameters, addenda, roots, and describing 
circles by the same rules that were given for spur-gears. 

Diameter of pinion = — ^ ^ ,, „ — = 5.09". 

d.l41b 

Diameter of the large gear = — — = 6.37". 

Diameter of describing circle = — — = 1.91". 

Take this as lyf inches, as in the last plate. 

Addendum = .3 inch ; root = .4 inch. The sectional view^ 
must be drawn first. Draw" P P' and through some point P' 
on this line draw" P' P^ perpendicular to it. Lay off P P' 
equal to the diameter of the pinion = 5.09 inches ; also P' P^ 
equal to the diameter of large gear = 6.37 inches. Bisect 
P P' and P' Pj, and draw^ M and ON perpendicular to those 
lines at the point of bisection ; they intersect in 0. M and 
N are the axes of the two gears, and intersect at right angles 



MECHANICAL DRAWING. 35 

as required. Draw POP, and P' 0. Through P draw APM 
perpendicular to OP. Through P' draw M P' N perpendicular 
to OP', and through P, draw P^ A^ perpendicular to P^. PM 
and P' M intersect at J7, on the line M ; P' X and P, A^ inter- 
sect at T, on the hue S. Lay of! P' C , P C\ and P,C^, each 
equal to 2 inches, or the width of the face of the teeth ; these 
lines are called the pitcli lines, and the Avidth of the face of 
the teeth is always measured on these lines. Lay off P. 4 equal 
to .3 inch =^ the addendum, and P B equal to .4 inch = the 
root. La}^ off P' E and P' D for the addendum and root of 
tlie other side, and P' E' and P' D^ for the addendum and root 
of the large gear. All of these addenda and roots are each 
equal to .3 inch and .4 mch, respectively. In bevel-gears, all 
straight lines of the tooth j^rofiles pass through the point of 
intersection of the axes ; hence, draw A 0, and A A' will be 
the projection of the top of the tooth. Draw BO, and B B' 
will represent the bottom of the tooth, the line A' C B' being 
perpendicular to OP. Make BE', D F, D^E^, etc. each equal 
to J inch, according to dimensions. Join E' , E, E^, and E^ 
Avith 0, intersecting the perpendiculars through C, C", and C, 
(namely, the lines A' C B\ etc. produced) at G', G, G^, and G.-^. 
G' G and G^ G.^ will represent the bottom of the gears. The 
rest of the sectional part can be drawn from the dimensions. 
To show the shape of the teeth proceed as follows : 
For the large gear, take A^ as a center, X P' as a radius, and 
describe an arc. Choose a point H, and lay off II H' = .48 
times the pitch = .48 inch, or the width of the tooth. With 
iV£" and XD^ as radii, describe the addendum and root circles. 
Roll the describing circles upon the arc whose radius is A^P', 
and construct the tooth profile in exactly the same manner as 
in Fig. 4 of the plate entitled Profiles of Gear-Teeth, Q II and 
Qj H' being the radii of the faces and flanks. To show the 
shape of the same tooth at C, draw C X perpendicular to 
OP', or, what is the same thing, parallel to A' P'. ^^'ith A'' C 
as a radius, and A" as a center, describe an arc. Draw XH 
and XH', and the distance between the points of intersection 
on the arc just drawn, measured on that arc, will l)e the pitch 
of the gear at the bottom of the tooth. With the same center, 



36 MECHANICAL DRAWING. 



arid N' E^ and N' E.^ as radii, describe arcs representing the 
addendum and root circles. Draw N Q and N Q^^ also QiiTand 
Q, H'. Through K draw K Q' parallel to H Q, and through K' 
draw K' Q.^ parallel to H' Q^ ; the points of intersection Q' and 
Q2 of these lines with NQ and NQ^ are the centers for the face 
and flank of the tooth at K and K'. Circles passing through 
these points concentric Avith N contain the centers of all the 
circular arcs forming the tooth profiles that may be laid off 
upon the arc whose radius is N K. The whole process is called 
develoijiiig" tlie teeth of bevel-gears. 

In the same manner construct the tooth curves for the pinion, 
using the same describing circles, lyf inches in diameter, and 
3TP', M'C as radii, instead of N P' and N' C . 

To construct the other view, draw first the projection of the 
pinion. Draw the center line mn. Produce the lines F F' ^ D B, 
P' P, and EA across the drawing, as shown. Choose a point 
S on inn as a center, and draw a quadrant with a radius equal 
to the radius of the pinion, as S P. Project the points D and E 
upon MO in D^ and E^. With aS' as a center, and the distances 
E^ E and Dg D as radii, describe quadrants to represent the tops 
and bottoms of the teeth, that is, the projection of the adden- 
dum and root circles of the pinion in Fig. 2. Since the whole 
pinion contains 16 teeth, the quadrant will contain 4 ; hence, 
divide the quadrant into 4 equal parts on the pitch circle to 
represent the centers of the teeth. Lay off on each side of the 
points of division distances ge and gh^ each equal to one-half 
the thickness of the tooth. On each side of the points of 
division on the addendum circle la}- off hf and /? c, each equal 
to one-half the thickness of the top of the tooth J K^ Fig. 1, 
measured on the addendum circle. On each side of the points 
of division on the root circle lay off / d and / a, each equal to 
one-half the thickness of the tooth at the root, as OP, Fig. 1, 
measured on the root circle. Having now three points on each 
side of all the teeth to the right of the center line mn^ project 
them upon the lines EA^ P' P, and D P, produced as shown. 
For example, project / and c upon EA in /' and c' ; e and 6 
upon P' P in ef and 1/ ; d and a ujDon D B in d' and a\ Draw 
a curve through these points either by using an irregular curve 



MECHANICAL DRAWING. 37 

or by circular arcs. This remark also applies to the other 
curves shown in the quadrant. 

The tooth curves in Fig. 1 must be drawn as accurately as 
possible, but those shown in Fig. 2, being oblique projections, 
are drawn to satisfy the eye, and no particular accuracy is 
required. To find the points on the tooth curves at the bottom 
of the pinion, describe a circle having a center Og upon mn, 
which shall be tangent to PP', and have a diameter equal to 
6.37" =z the diameter of the large gear. Through B' and A\ 
Fig. 1, draw lines parallel to 0.^ ; also draw other lines through 
0^ and the points d',f', c', etc., cutting the lines first drawn in 
f/", f, c", etc. Two points are considered enough in this case, 
as the curves are very short. They may be drawn in with the 
irregular curve in the same manner as the tops. The other 
teeth are drawn in a similar manner. Draw the middle tooth 
first. The left-hand half of the pinion is exactly the same as 
the right-hand half. 

To draw the projection of the large gear, project the points 
E', D^, L, and R upon the axis ON, in the points E^, D^, L^, 
and R^, and with 0.^ as a center, and radii equal to E^E\ D^D^, 
L^ jL, and R^ R, describe circles to represent the addendum 
and root circles of the tops and bottoms of the teeth in Fig. 2. 
Divide the pitch circle into 20 equal parts to correspond with 
the number of teeth in the large gear, beginning with the point 
of intersection of the pitch circle with the center line m n. Lay 
off on each side of these pitch-circle divisions, distances equal 
to one-half the thickness of the teeth = one-half of HH' in 
Fig. 1. By exactly the same method that was used to lay ofif 
the thickness of the teeth at the top and bottom on the quad- 
rant, lay off the thickness of the top and bottom of the teeth on 
the addendum and root circles in Fig. 2. Draw the bottoms of 
the teeth in exactly the same manner as the bottoms of the 
pinion teeth were drawn. 

All of the teeth of the large gear are alike in the projected view. 

Bevel-gears are always measured according to their largest 
pitch diameter, as P P' and P' P^. If a bevel-gear were spoken 
of as 12 inches in diameter, it would be understood that the 
largest pitch diameter was 12 inches. 



38 MECHANICAL DRAWING. 



DRAWIN^G PIRATE, TITJ.T] : GOVERKOR. 

69. Tliis plate hIiows a partial section and elevation of a 
governor of the Porter- Allen t^^pe. A belt driven from a 
pulley on the crank-shaft causes the pulley A to revolve, which 
in turn drives the bevel-gears ; the bevel-gears drive the vertical 
shaft i?, and cause the balls C, C to revolve. Owing to the cen- 
trifugal force generated by the balls, they tend to fly outwards 
and raise the weight TF, which fits loosely on the shaft B. 
When the engine is running at its rated speed the balls C, C are 
22 inches apart between their centers, or each is 11 inches from 
the center line m n. If the engine runs slower than its rated 
speed the centrifugal force becomes less, and the weight W 
causes the balls to move inwards ; the w^eight W drops and 
forces down the lever arm i), which admits more steam to the 
cylinder, and increases the speed of the engine. If the engine 
runs faster than its rated speed the centrifugal force increases, 
raises the weight IF, and lifts the lever arm D, which shuts off 
steam admitted to the cylinder, and decreases the speed of the 
engine. In both cases the other lever arm actuates the valve 
by means of mechanisms not shown. 

To draw the governor as shown, draw the center line mn and 
the base line, and locate the top of the shaft. Then, draw all 
that part of the figure that is sectioned. The brass oil cup has a 
thread cut on its lower end, and is screwed in by means of the 
hexagonal shoulder. The tap bolt F' holds the plate F in 
place. This plate can be removed so that the gears, bearings, 
etc. may be examined. 

To draw the upper part (not sectioned) from the dimensions 
given, proceed as follows : Locate the center of the arms 
2y\ inches below the top of the shaft. Draw a horizontal line 
H H^ 8f inches above the top of the body or sectional part, and 
mark off on it the point Q, 2J inches to the left of m n. W^ith 
Q and as centers, and radii of 13^^ and 16f inches, 
respectively, describe short arcs intersecting at P ; QP and P 
are the center lines of the governor arms. The corresponding 
points on the other side are found in the same manner. Hav- 
ing located the points 0, P, and Q, the rest of the drawing can 



MECHANICAL DRAWING. 39 

be completed without further description from the dimensions 
given, /and K are washers. 

The upper end of the shaft has a long hole drilled in it to 
lubricate the bearing surface between the weight and the shaft. 
The lower end of the shaft turns in a brass bearing, and has two 
hardened steel convex disks between it and the bearing. These 
disks reduce the wear caused *by the friction due to the weight 
of the shaft, arms, and weight W. 



DRAWI:N G PI.ATE, TITLE : BOILER SETTIIS^G— I. 

70. Tliis plate shows a front view of a battery of three 
return tubular boilers, one in elevation and the other two 
in section. When drawing this plate, reference must be made 
occasionally to the next jilate, which is sent with it for the pur- 
pose of giving the student an opportunity of ascertaining some of 
the dimensions, and of obtaining a clear idea of how the sections 
are taken, and the reasons for drawing certain lines. Since 
both plates have the same title and are distinguished only by 
the numerals I and II, they will hereafter be referred to as I or 
II, as occasion may arise. 

In II is shown a section taken on the vertical center line of 
the setting of one of the boilers shown in I, the boiler itself 
being shown in side elevation. Fig. 1 shows a front elevation 
of one of the boilers ; Fig. 2, a section taken through the smoke- 
box on the lines sr and qp ; and Fig. 3, a section on the line st. 
(SeelL) 

71. To draw I, begin by drawing the main horizontal center 
line mil at a distance of about 7^ inches from the bottom border 
line of the drawing ; locate the point 0, the center of the boiler, 
in Fig. 2, on the horizontal center line m n, somewhere near the 
center of the sheet, and draw the vertical center line sr through 
it. Lay off points 0' and 0" in the main horizontal center line 
m n, at a distance of 6 feet 7^ inches on each side of the vertical 
center line s r. Through these points draw the vertical center 
lines qp and vt of the boilers in Figs. 1 and 3, respectively. 



40 MECHANKUL DRAWING. 

Next laj'^ off, above and below the main horizontal center 
line )».7i, the distances nh = 3 feet 5 J inches and nd = 
6 feet 7J inches, which are to be taken from II, and draw the 
lines ah and cd^ respectively. From the vertical center line qp 
lay off to the right a distance of 3 feet 7f inches, and to the left 
a distance of 3 feet 3f inches, and draw the lines db and fe. 
With 0' as a center, and one-half of 3 feet 9 inches as a radius, 
describe the inner circle of the smokebox doors, and complete 
them from the dimensions given. Then lay off the centers of 
the furnace doors, at a distance equal to 18 inches on each side 
of the vertical center line qj), and draw vertical center lines 
through them. Also, draw the horizontal center line of these 
doors at a distance of 3 feet 3 inches below the main horizontal 
center line mn. The student now has the location of the 
furnace doors, and should experience no trouble in completing 
them from the dimensions given. Having finished these doors, 
he should then draw in the ash-pit doors and complete the 
boiler front. 

Some of the small boiler fixtures, such as the steam gauge, 
water column, water gauge, water-gauge cocks, etc., are not 
dimensioned, so as not to obscure the drawing by the use of 
too man}^ lines and figures. They should be proportioned by 
the eye. This is the custom followed in the drafting rooms. 
On completing these he should draw in the smokestack and its 
base, then the dome, omitting the rivets. The dimensions of 
the dome can be obtained from Fig. 3 and II. The drawing 
of the rivets will be taken up later. 

To draw Figs. 2 and 3, begin by drawing in the boilers with 
the tubes, brackets, and domes complete. There are 24 rivets 
around the upper edge of each dome. These may be drawn in 
their correct position as shown, by producing the center line 
V t in Fig. 3 upwards, taking some point on this line as a center, 
and describing a circle having the same diameter as the dome. 
Divide this circle into 24 equal parts, using the vertical center 
line for the starting point, and project the points of division of 
the lower half of the circle downwards upon the horizontal cen- 
ter line of the rivets. The points thus projected upon this line 
will be the centers of the rivets. Onlv the rivet on the center 



MECHANICAL DRAWING. 41 



line V t will be round in this view, all of the others being elHpti- 
cal, and may be drawn free-hand. Then draw in the walls. The 
surfaces of these walls which come in contact with the fire and 
hot gases are lined with firebrick, and the walls proper are made 
of red brick. The ordinary red brick is sectioned in the same 
manner as cast iron, while the sectioning of the firebrick is a 
heavy line and a short broken line, alternately. Next, draw in 
the plates and rollers on which the boiler rests. These rollers 
are used to allow the boilers to expand and contract freely 
under the usual influences of alternate heat and cold. 

Since Fig. 2 is a section taken through the smokebox on the 
lines s r and f/p, II, and the inside of the smokebox, except the 
top of it, is built up of firebrick in the shape of a frustum of a 
cone, as will be seen by referring to Plates I and II, the diam- 
eter of the smokebox on the line Avhere the section is taken 
is smaller than the diameter of the boiler, and is equal to a 
radius gh (see II), which measures 2 feet 1^ inches. This 
accounts for part of the boiler being shown in dotted lines. 

In I, the location of the holes receiving the pipes connected 
to the water column is shown by / and J, and the hole receiving 
the feed-pipe b}^ k. Now draw in the smokestack, its base, 
and the frames of the furnace doors from the dimensions given, 
and complete this figure. In Fig. 3, draw in the safety valve 
and grate bars, obtaining some of the dimensions from II. 

Draw in the buckstaves A and B and the tie- rods / / and l^ l^ ; 
also the buckstaves C, D, and E at the back of the boilers, 
shown by dotted lines, and the tie-rods u, u, u, etc. These rods 
are rectangular in cross-section and have round end pieces, so 
that they will admit of being threaded to receive the nut. 
Buckstaves are used for strengthening the walls of the boiler 
setting and preventing them from bulging outwards. 



DRAWIXG PLATE, TITLE: BOII.TCR SETTI1S"(;— II. 

72. In drawing this plate, reference must be made occasion- 
ally to the previous i)late for some of the dimensions. Begin 
by drawing the main horizontal center line m n ; then the shell 



42 MECHANICAL DRAWING. 



of the boiler from the dimensions given ; after which draw the 
center line v t of the dome exactly in the center of the middle 
section of the boiler shell, and complete the dome. The rivets 
in the dome and boiler shell may be drawn in the same manner 
as explained in I. 

To draw the curves representing the intersection of the dome 
with the boiler, locate the point v' on the center line v t corre- 
sponding to the point v' ^ in Fig. 3, Plate I ; and on the center 
line V t of the dome in II, find by trial the point 0, so that 
when it is used as a center, an arc may be passed through the 
point v' and the two points w, iv. The radius of this arc will be 
3 feet 3 inches. These dimensions should not appear on the 
student's drawing. The edge of the flange of the dome may 
also be described from the same center. It is not necessary to 
construct the true curve of the intersection of the dome and the 
shell, as drawn in Fig. 1 of the plate entitled Intersections and 
Develo23ments. 

Draw the yoke on the top of the dome, after which draw the 
brackets and safety valve from the dimensions given on I and 
II. Below the main horizontal center line m n, lay off a dis- 
tance of 6 feet 7J inches, and draw the line c' d\ and above this 
line (c' d') lay off the height h of the boiler setting = 10 feet ^ 
inch, and draw the line a' h' . On the main horizontal center 
line mn lay off to the left from the front head of the boiler a 
distance of 15J inches, and draw the vertical line e' e', after 
which complete the boiler front from the dimensions given, 
referring to I when necessary. On the same center line, lay off 
to the right from the back head of the boiler a distance of 24 
inches, and draw the vertical line/'/'; after which complete the 
rear wall, and then draw the flue plate g' . Now draw in 
the grate bars, bridge, blow-off pipe, and smokestack, including 
the base, from the dimensions given, and, finally, the small 
fixtures, such as the water column and connections, steam 
gauge, water-gauge cocks, etc., also the feed- water pipe. No 
dimensions are given for these, and, therefore, they must be 
proportioned by the eye. Then draw in the buckstaves and 
tie- rods. The student should experience no difficulty in com- 
pleting this plate. 



MECHANICAL DRAWING. 43 



TRACHNTGS. 



73. In actual practice in the drawing room, it is necessary 
to have more than one copy of a drawing. It would be very 
expensive to make a finished drawing every time an extra 
copy was wanted, and, to avoid this, tracings and blue-prints are 
made. Any number of blue-print copies can be made from the 
same tracing. A comj^lete pencil drawing is made first ; then, 
instead of inking in as heretofore, a piece of tracing paper or 
tracing cloth of the same size as the pencil drawing is fastened to 
the board over the original drawing. The tracing paper or 
cloth being almost transparent, the lines of the drawing can be 
readily seen through it, and the drawing is inked-in on the 
tracing paper or cloth in the same manner as if inking-in a 
finished drawing. 

Tracing paper is but little used in this country. It is 
easily torn, and cannot be preserved as well as tracing cloth. 
The two sides of the tracing clotli are known as the glazed 
side and the dull side ; they are also known as the front and 
the back. The glazed side, or front, is covered with a prepara- 
tion that gives it a very smooth polished surface ; the back, or 
dull side, has very much the appearance of a piece of ordinary 
linen cloth. Either side may be used for drawing upon, but 
when the glazed side is used, care must be taken to remove all 
dirt and grease, otherwise the ink will not flow well from the 
pen. This can be done by taking a knife or a file and scraping 
or filing chalk upon the tracing cloth ; then, take a soft rag of 
some kind — cotton flannel or chamois skin — and rub it all over 
the tracing cloth, being sure to rub chalk over ever}^ spot. 
Finally, dust the rag and remove as much of the chalk from 
the cloth as can be gotten off by rubbing with the rag. The 
finer the chalk jDowder is, the better. It is not usual to chalk 
the dull side, but it improves it to do so. The glazed side takes 
ink much better than the dull side, the finished drawing looks 
better and will not soil so easily, and it is also easier to erase a 
line that has been drawn on this side. Pencil lines can also be 
satisfactorily drawn on the dull side, and if it is desired to 
photograph the drawing, it is better to draw on this side. The 



44 MECHANICAL DRAWING. 

draftsman uses either side, according to the work he is doing, 
and to suit his individual taste, but if the glazed side is used, it 
must be chalked. The tracings are drawn in a manner similar to 
the finished drawings, the center lines, section lines, etc. being 
drawn exactly as j)reviously described. 

After having drawn the plate entitled Boiler Setting — II, the 
student should make a tracing of the plate entitled o-inch 
Globe Valve. 

BIii;E-PRi:N^Ti:NG. 

74. Blue-printing is the process of duplicating a tracing by 
means of the action of light upon a sensitized paper. The follow- 
ing solution is much used for sensitizing the. paper : Dissolve 
2 ounces of citrate of iron and ammonia in 8 ounces of water ; 
also, 1 J ounces of red prussiate of potash in 8 ounces of water. 
Keep the solutions separate, and in dark-colored bottles in a 
dark place where the light cannot reach them. Better results 
will be obtained if ^ an ounce of gum arable is dissolved in each 
solution. 

When ready to prepare the paper, mix equal portions of the 
two solutions, and be particularly careful not to allow any more 
light to strike the mixture than is absolutely necessar}^ to see 
by. For this reason, it is necessar}^ to have a dark room to 
work in. There must be in this room a tray or sink of some 
kind that will hold water ; it should be larger than the blue- 
print, and about 6 inches deep. There should also be a flat 
board large enough to cover the tray or sink. If the sink is 
lined with zinc or galvanized iron, so much the better. There 
must be an arrangement like a towel rack to hang the prints on 
while they are drying. For the want of a better name, this 
arrangement will be called a print rack. The paper used for 
blue-printing should be a good, smooth, white paper, and may 
be purchased of any dealer in drawing materials. Cut it into 
sheets a little larger than the tracing, so as to leave an edge 
around it when the tracing is placed upon it. Place eight or 
ten of these sheets upon the flat board before mentioned, taking 
care to spread flatty one above another, so that the edges do not 
overlap. Secure the sheets to the board by driving a brad or 



MECHANICAL DRAWING. 45 



small wire nail through the two upper corners sufficiently far 
into the board to hold the weight of the papers when tlie board 
is placed in a vertical position. Lay the board on the edges of 
the sink, so that one edge is against the wall and the ])oard is 
inclined so as to make an angle of about 60° with the horizontal. 
Darken the room as much as possible, and ol^tain Avhat light 
may l)e necessary from a lamp or gas jet, which should be 
turned down very low. With a wide camel' s-hair brush or a 
fine sj^onge, spread the solution just prepared over the top sheet 
of paper. Be sure to cover every S23ot, and do not get too much 
on the paper. Distril)ute it as evenly as joossible over the 
paper, in much the same manner that the finishing coat of 
varnish would l^e put on b}^ a painter. Remove the sheet by 
pulling on the lower edge, tearing it from the nail which holds 
it. and place it in a drawer where it can lie fiat and be kept 
from the light. Treat the next sheet, and each succeeding sheet, 
in exactly the same manner, until the required number of 
sheets has been prepared. 

Unless a large number of prints is constantly used, it is 
cheaper to buy the paper already prepared. It can be bought 
in rolls of 10 yards or more, of any width, or in sheets already 
cut and ready for use. There is very little, if anything, saved 
in preparing the paper, and better results are usually obtained 
from the commercial sensitized paper, since the manufacturers 
have machines for applying the solution, and are able to dis- 
tribute it very evenh\ 

75. In Figs. 76 and 77 are shown two vicAVS of a printing 
frame which is well adapted to sheets that are not over 
17" X 21". The frame is placed face dow^nw^ards, and the 
back A is removed by unhooking the brass spring clips B, B 
and lifting it out. The tracing is laid upon the glass C, with 
the inked side touching the glass. A sheet of the prepared 
paper, perfectly dry, is laid upon the tracing with the yellow 
(sensitized) side downwards. The paper and tracing are 
smoothed out so as to lie perfectly fiat upon the glass, the cover 
A is replaced, and the brass spring clips B^ B are sprung under 
the plates D, so that the back cannot fall out. While all this 
is being done, the paper should be kept from the light as much 



46 



MECHANICAL DRAWING. 



as possible. The frame is now placed where the sun can shine 
upon it, and adjusted as shown in Fig. 77, so that the sun's rays 
will fall upon it as nearly at right angles as possible. Accor- 
ding to the conditions of the sky— whether clear or cloud}^ — 
and the time of the year, the print must be exposed from 3 to 
15 minutes. The tray, or sink, already mentioned, should be 
filled to a depth of about 2 inches with clear water (rain water 
if possible). The print having been exposed the proper length 
of time, the frame is carried into a dark part of the room, the 




Fig. 76. 



cover removed, and the print (prepared paper) taken out. Now 
place it on the water with the yellow^ side doAvn, and be sure 
that the water touches every part of it. Let it soak while put- 
ting the next print in the frame. Be sure that the hands are 
dry before touching the next print. The first print having 
soaked a short time (about 10 minutes) take hold of two of its 
opposite corners, and hft it slowly out of the. water. Dip it 
back again and pull out as before. Repeat this a number of 
times until the paper appears to get no bluer ; then hang it by 



MECHANICAL DRAWING. 



47 



two of its corners to dry on the print rack above spoken of. If 
there are any dark purple or bronze-colored spots on the prints, 
it indicates that the prints were not washed thoroiighl}^ on 
those spots. If these spots are well washed before. the print is 
dried, the}^ will disappear. 




Fig. 



76. It is best to judge of the proper time of exposure to the 
light by the color of the strip of print projecting beyond the 
edge of the tracing. To obtain the exact shade of the projecting 
edge, take a strip of paper about 12 or 14 inches long and 3 or 
4 inches wide. . Divide it into, say, 12 equal joarts by lead-pencil 
marks, and, with the lead pencil, number each part 1, 2, 3, etc. 
Sensitize this side of the paper, and, after it has been properl}' 
dried, place it in the print frame with tlie sensitized side and 
the marks and figures against the glass. Expose the whole 
strip to the light for one minute ; then cover the part of the 
strip marked 1 with a thin board or anything that will prevent 
the light from striking the part covered. At the end of the 
second minute, cover parts 2 and 1 ; at the end of the third 



4.8 



MECHANICAL DRAWING. 



minute, parts 3, 2, and 1, etc. When twelve minutes are up, 
part 1 will have been exposed one minute ; part 2, two minutes, 




Fig. 



etc., part 12 having been exposed twelve minutes. Remove 
the frame to a dark part of the room, and tear the strip so as to 
divide it into two strips of the same length and about half the 



MECHANICAL DRAWING. 49 

original widtlh Wash one of the strij)s as before described, 
and when it has (hied, select a good rich shade of blue, neither 
too light nor too dark ; notice the number of the part chosen, 
and it will indicate the length of time that the i)rint was 
exposed. Examine carefully the corresponding part of the 
other strip, and the correct color of the edge of the print pro- 
jecting beyond the tracing is determined. All prints should be 
exposed until this color is reached, no matter how long or how 
short the time may be ; then they should be immediateh^ taken 
out and washed. 

In Fig. 78 is shown a patented frame which can be shoved 
out of the window and adjusted to any angle. When not in 
use, it can be folded up against the wall, and occupies but 
little space. It is made in different sizes from 16" X 24" to 
48" X 72". It is one of the best frames in the market, and is 
placed in such a position relatively to the window that the 
window can be lowered to the top of the main arm, when it is 
desired to keep out the cold during the winter. 



DRAWIXG PJLATE, TITI^E : SIX-HORSEPOWER 
HORIZOXTAL STEAM E:N^GIXE. 

77. Instead of making a finished drawing of this engine, as 
in the previous plates, from an exact copy, the student is given 
the rough sketches of the details of a slx-liorsepower liori- 
zontal steam eiig-ine, with full dimensions marked upon 
them ; from these he is expected to make a general pencil draw- 
ing of the engine in two views — a plan and a side elevation. 

The pencil drawing should then be traced according to the 
directions previously given. The details are not drawn to scale, 
but are fully dimensioned. In order to draw the engine to as 
large and as convenient a scale as possible, it is necessary to 
make this tracing a trifle larger than the plates which have pre- 
ceded it. The size over all will be 14|" X 18^", with the usual 
border line ^ inch from each edge all around. 

That the student may have a good idea of what he is expected 
to do, a greatly reduced cut of the general drawing is also given 
him. All dotted lines indicating parts not seen have been 



50 MECHANICAL DRAWING. 

oinitted, in order to simplify the work. The scale to ])Q used is 
3 inches = 1 foot. 

Draw the 'center lines mn, p q^ r s, and t r. Draw the side 
elevation of the bed-plate with the l)earing caps in position, 
from the dimensions given on the detail sketches, taking care 
to make those parts which ai-e likely to be hidden by the fly- 
W'heel, eccentric rod, etc., light so that they ma}^ be easih^ 
erased before tracing. The drawing may be traced without 
removing the unnecessary construction lines, but it is better to 
do so, since it lessens the liability of inking-in lines which will 
have to be erased from the tracing. 

Draw the plan of the bed-plate wdth the bearing caps, studs 
and nuts, foundati@n-bolt holes, etc., shown in their proper 
places and positions. The different curves of the bearing caps 
in the plan should be constructed by projecting points from the 
view^ shown in the side elevation. In actual practice in the 
drawing room, three or four of the principal points (those which 
mark the limits) w^ould be located and the curves sketched in 
free-hand, they being inked-in on the tracing b}^ aid of an 
irregular curve. In such cases the draftsman has a good idea 
of the shape of the curves, owing to previous practice in drawdng 
them. When drawing in the curves formed by the opening in 
the bed-plate, shown in this view, the student must exercise 
his own judgment regarding their shape, taking care not to get 
them too straight. The general drawing gives a good idea of 
their proper curvature. 

Returning to the elevation, draw" the crank and crank end of 
the connecting-rod in the position shown in the general draw- 
ing. With the center of the crank-pin as a center and a radius 
equal to the length of the connecting-rod between its centers 
(obtained from the detail sketch), describe an arc cutting the 
center line p q at a point which will be the center of the cross- 
head pin. Draw the cross-head, obtaining the dimensions 
from the detail sketch. Complete the connecting-rod in both 
view^s and draw the piston rod 1 inch in diameter. Draw" both 
views of the cylinder wdth the nuts and the steam pipe in their 
proper position, getting all dimensions from the detail sketches. 

Draw the center line of the valve stem in the plan vicAv, and 



MECHANICAL DRAWING. 51 



draw the stuffing-box, valve stem, valve-stem slide and its 
guide in botli views. In order to determine the position of the 
valve-stem slide, it is necessary to locate the center of the 
eccentric. Referring to tlie general drawing, it is seen that 
the eccentric is on the dead center farthest from tlie cylinder. 
The offset of the eccentric is given as f inc]i in tlie detail 
sketch ; hence, when in this position, the center of the eccentric 
strai^ will be situated J inch to the right of the crank-shaft 
center on the line j) g. Witli this point as a center and a radius 
equal to the distance between the centers of the eccentric strap 
and the hole in the stub end of the eccentric rod (see detail 
sketch), in this case 2 feet 4-g- inches, describe an arc cutting 
the center line j) 7 in ; will l)e the center of the pin on the 
valve-stem slide, which may be completed by aid of the detail 
sketch. Complete the drawing of the eccentric, eccentric strap 
and eccentric rod in both views. 

Finally, draw in the band-Avheel and fly-wheel (see general 
drawing for position). The fly-wheel will be of the same diam- 
eter as the band-wheel, l^ut only 3 inches wide. 

The pencil drawing is now completed. Before beginning to 
trace, erase those lines which are not to be inked-in. This is 
not necessary, but it is better to do so, since it avoids confusion 
and lessens the liabilitv of making mistakes. Some draftsmen 
prefer to redraw a portion of those parts Avhich are to be inked 
in with a somewhat softer pencil, and leave the light construc- 
tion lines on the drawing rather than erase them ; in some 
cases, this saves time. 

The preliminary directions for tracing a drawing have been 
given previoush^ First, trace the side elevation, beginning 
with the fly-wheel, and then as much of the connecting-rod, 
eccentric, and eccentric rod as can be seen. Trace all those 
parts of the bed-plate, cylinder, valve stem, stuffing-box, etc. 
that are seen. Then trace the plan view, letter the drawing, 
and draw the border lines. There will be no plate number for 
this tracing, but the student's name, class number, and the 
date of completion will be put on as before. 

The student should exercise particular care to have every 
dimension scale exactly the size given in the detail sketches. 

V. 



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